Abstract
Elementary Theory of Computation. The Mathematical Concept of Algorithm. Church's Thesis. Universal Programs and the Recursion Theorem. Complexity of Algorithmic Unsolvability. Recursively Unsolvable Problems. The Arithmetical Hierarchy and Degrees of Unsolvability. Abstract Complexity of Computation. Recursiveness and Complexity. Complexity Classes of Recursive Functions. Complexity Classes of Primitive Recursive Functions. Polynomially- and Exponentially-Bounded Complexity Classes. Finite Automata. Context-Free Languages. Elementary Predicate Logic. Logical Analysis of the Truth Concept. Syntax and Semantics. Completeness Theorem. Consequences of the Completeness Theorem. Logical Analysis of the Concept of Proof. Gentzen's Calculus LK. Cut Elimination for LK. Consequences of the Cut Elimination Theorem. Complexity of Logical Decision Problems. Undecidability and Reduction Classes. Incompleteness of Arithmetic. Recursive Lower Complexity Bounds. Bibliography. Index.
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